Answer:
A.
B.
Step-by-step explanation:
We have been given bases of two triangular prisms.
A. Since we know that volume of triangular prism is base area of the prism times height of the prism.
Since base of our given prism is right triangle, so area of the base of prism will be:
Upon substituting our given values in volume formula we will get,
Therefore, volume of the prism made by triangle PQR is 12960 cubic inches.
B. Let us assume that both prism are similar, so we can use proportions to solve for the volume of triangle XYZ.
Let us find the proportion between the sides of both triangles.
Since for volume of triangular prism we multiply base area and height of the prism, this means we will have to multiply the proportion of each side length 3 times to find the proportion of volumes between our both prism.
So we can set proportion for volume of both prisms as:
Upon substituting volume of prism made by triangle PQR we will get,
Let us multiply both sides of our equation by 7776 cubic inches.
Therefore, the volume of prism made by triangle XYZ is 2304 cubic inches.
Answer:
About 473 quails.
Step-by-step explanation:
Exponential equation with as the initial amount and rate of r is:
After 5 years the population will be:
So the population will be about 473 quails.
Answer:
Step-by-step explanation:
- grateful
- grate
- gulf
- rate
- tar
- ear
- tag
- rate
- rag
- get
- eat
- ale
- ate
- leg
- rug
- tea
- fate
- gate
- gae
- gul (idk about his one. it is a scrabble word tho)
- lea
- tera
Answer: A: 6:14
C: 15:35
E: 30:70
Step-by-step explanation:
From the question, we are given that the ratio of the number of adults to the number of children at the resturant is 3:7.
The choices below that represent an equivalent ratio goes thus:
A: 6:14
This can be represented as: 6/14. The common factor is 2 and we reduce to lowest term which would be: = 3/7 = 3:7
This is an equivalent ratio.
B: 8:12
This can be represented as: 8/12. The common factor is 4 and we reduce to lowest term which would be: = 2/3 = 2:3
This is not an equivalent ratio.
C: 15:35
This can be represented as: 15/35. The common factor is 5 and we reduce to lowest term which would be: = 3/7 = 3:7
This is an equivalent ratio.
D: 21:9
This can be represented as: 21/9. The common factor is 3 and we reduce to lowest term which would be: = 7/3 = 7:3
This is not an equivalent ratio.
E: 30:70
This can be represented as: 30/70. The common factor is 10 and we reduce to lowest term which would be: = 3/7 = 3:7
This is an equivalent ratio.
The correct options are A, C,and E.
Answer:
Step-by-step explanation:
In an arithmetic sequence, we are given that:
The nth term of an arithmetic sequence,
When n=17, , we have:
82=a+(16)(-6)
82=a-96
a=82+96
a=178
Therefore, the 10th term of the sequence